Question

How do you find the exact value of sin 105 degrees?

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Answer 1

Answer:

sin (105) = sin (15 + 90) = cos 15. Apply the trig identity: cos2x=2cos2x−1. sin(105)=cos(15)=√2+√32. Check by calculator.

Answer 2

Answer:

The exact value of sin105° is $\frac{\sqrt{6}\ +\sqrt{2} }{4}$.

Step-by-step explanation:

Given, sin 105°

It can also be written as

sin 105° = sin(60° + 45°)

As we know the trigonometry formula,

sin(A + B) = sinAcosB + cosAsinB

using this formula, we get

sin 105°

= sin (60° + 45°)

= sin 60° cos45° + cos 60° sin45°

= (√3/2)×(1/√2) + (1/2)×(1/√2)

= √3/2√2 + 1/2√2

= (√3 + 1)/2√2

= (√6 + √2)/4

Hence, the exact value of sin 105° is (√6 + √2)/4.

Sin 105 degrees has a numeric value of 0.96592. The equivalent angle in radians to the given angle (105 degrees) can also be used to define sin (1.83259).

To learn more about sine & cosine, click on the link below:

https://brainly.in/question/48719490

To learn more about the trigonometry, click on the link below:

https://brainly.in/question/2685053

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